FIG. 1 illustrates a conventional inkjet printing system 1 including an ink jet printhead 10, which is an example of an ink-ejecting marking device. The ink jet printhead 10 includes an ink-reservoir 19 with a plurality of nozzles 30 communicatively connected thereto via channels (32 for example), through which ink in the reservoir 19 is ejected in the form of drops (33, for example) from drop generators (not shown) onto a substrate 20. Depending upon the contents of an image 12 to be formed on the substrate 20, a driving circuit 14 selectively applies a voltage waveform via an electrical pulse source 16 to the drop generators corresponding to particular nozzles of the nozzles 30. This selective application of a voltage waveform causes drops of ink (33, for example) to be ejected from the particular nozzles, thereby causing the image to be formed on the substrate 20. Conventionally, each drop generator is a heater resistor (not shown) having a resistance R. For a waveform consisting of a constant voltage pulse amplitude V and a pulsewidth t, for example, the power dissipated in the heater resistor is V2/R, and the energy dissipated in the heater resistor is V2t/R.
If the voltage applied by the controller 14 via the electrical pulse source 16 to the nozzles 30 is too high, the operational life of the inkjet printhead 10 is reduced, thereby causing premature failure. On the other hand, if the applied voltage is too low, the nozzles 30 will not fire reliably or will not fire at all. Accordingly, it is important in the art to be able to determine an appropriate voltage to be applied to the nozzles that reliably will cause the nozzles to fire while not excessively harming the operational life of the inkjet printhead 10.
One conventional scheme for determining an appropriate applied voltage is illustrated with FIG. 2. This conventional scheme involves printing a sequence of swatches 101, each having a same pattern-density (i.e., a same number of nozzles selected to be fired), but each being printed with a successively different applied-voltage. In the example of FIG. 2, the first swatch 102 is printed with a high voltage that fires all selected nozzles, and each successive swatch thereafter is printed with a slightly lower voltage until the last swatch 103 is printed with such a low voltage that none or a small percentage of the selected nozzles fire. (It should be noted that the texture of the swatches 101 shown in FIG. 2 is used merely to illustrate a change in reflectance of each swatch and is not used to illustrate exactly which nozzles fired and which did not.)
Continuing with the example of FIG. 2, the sequence of swatches 101 is then scanned by an optical scanner to determine which swatch exhibits a reflectance that is substantially lower than the previous swatch, in order to determine the voltage at which most nozzles reliably fire. To elaborate, FIG. 3 illustrates a graph of voltage applied to the selected nozzles versus reflectance of a swatch generated at that voltage. Although the graph of FIG. 3 illustrates a continuous function, a graph generated by data provided by the optical scanner reading the swatches illustrated in FIG. 2 would have discrete points 201-210, for example. The optical scanner reads the reflectance of the first swatch 102 to determine point 210, for example. Then, the optical scanner reads the reflectance of the second swatch to determine point 209, and so on. To determine an appropriate applied voltage, the first substantial difference between reflectances at successive points from point 201 to point 210 that exceeds a predetermined amount is flagged, and a point between the points that resulted in the first substantial difference of reflectances is selected as the appropriate applied voltage. In the example of FIG. 2, the difference in reflectances between the second swatch, corresponding to point 209 and the third swatch, corresponding to point 208 may be selected as the points that produce the first substantial difference in reflectance. Accordingly, a voltage inclusively between the voltages corresponding to points 209 and 208 may be selected as the appropriate applied voltage. Depending upon how the printhead 10 is to be calibrated, however, the reflectance difference between points 209 and 208 may not be substantial enough and, for example, the reflectance drop between points 208 and 207 instead may be used to determine the appropriate applied voltage.
A draw back of this conventional scheme is that measuring the reflectance of the swatches is dependent upon characteristics of the substrate upon which the swatches are printed. In particular, ink spreads and interacts differently depending upon the substrate being used. Accordingly, reflectance measurements for the same sequence of swatches will be different depending upon the substrate on which the swatches are printed. Further, reflectance measurements of swatches also are dependent upon ambient conditions, such as humidity and temperature. Accordingly, the same sequence of test swatches printed on the same type of substrate often are different depending upon the humidity and/or temperature of the environment in which they are printed. Accordingly, a need in the art exists for a method of determining an appropriate applied voltage that is independent of or reduces the impact of these factors.